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Full text of "The Pan Book of Mathematical Tables"

The Pan book of 
MATHEMATICAL 
TABLES 



1 



TP84 



compiled by 

A. MONTAGUEBEART 



An important new referen 
for the student and 
for everyone in the expanding 
technical professions 






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THE PAN BOOK OF 
MATHEMATICAL TABLES 






CONDITIONS OF SALE 

This book shall not be lent, resold, hired out 

or otherwise disposed of by way of trade in 

any form of binding or cover other than that 

in which it is published 



THE PAN BOOK OF 
MATHEMATICAL TABLES 

A. MONTAGUE-BEART 



£ 



A PAN ORIGINAL 



PAN BOOKS : LONDON 



First published 1965 by 

PAN BOOKS LTD 

8 Headfort Place, London, S.W.I 

© A. Montague-Beart, 1965 



Printed in Great Britain by Butler & Tanner Ltd., Fromc and London 



CONTENTS 



Logarithms 
Anti-logarithms 
Log. sines 
Log. cosines 
Log. tangents 
Log. cotangents 
Log. secants 
Log. cosecants 
Natural sines 
Natural cosines 
Natural tangents 
Natural cotangents 
Natural secants 
Natural cosecants 
Reciprocals 
Napierian logarithms 



sinh x 
cosh x 
Squares 
Square Roots 
Cubes 
Cube Roots 



page 
2 
6 
10 
14 
18 
22 
26 
30 
34 
38 
42 
46 
50 
54 
58 
62 
66 
68 
70 
72 
74 
78 
86 
90 



The Metric System: 

Measures of Length 
Measures of Capacity 
Measures of Weight 
Measures of Surface 
Cubic Measure 

Conversion Tables: 



page 

102 
102 
102 
102 
102 



Length 


103 


•Volume 


104 


Area 


104 


Mass 


105 


Linear Velocity 


105 


Density 


105 


Power Conversion Factors 


106 


Heat and Work Conversion Factors 


107 


Pressure Conversion Factors 


108 


Decimal equivalents of fractions 


109 


Inches to decimals of a foot 


110 


Temperature Conversion 


112 


Pressure Conversion Table 


114 


Viscosity Conversion Table 


115 


Speeds of Flow of Water 


116 


Material Densities 


117 


Relative Humidity Tables 


121 


Atomic Weights— Physical and Chemical Tables: 




The Periodic Table 


128 


Properties of Solids 


131 


Properties of Liquids 


132 


Properties of Gases 


133 


Properties of the Elements 


134 


International Temperature Scale 


138 


Atomic and Molecular Constants 


139 



page 
Radioactivity 140 

Table of Elements and Mass Numbers of the Isotopes 145 
The Particles of Modern Physics 151 

Energy Equivalents 155 



Optical Data: 

Refractive Index of Gases 
Refractive Indices for Mean D Line 
Wavelengths of Important Spectral Lines 
The Electromagnetic Spectrum 

Acoustic Data! 

Velocity of Sound 
Loudness of Sounds 
Music 

Geometrical Mensurations 
Surfaces and Volumes of Solids 



156 
156 
156 
157 



158 
158 
158 

159 
168 



VI 



vii 



ACKNOWLEDGEMENTS 

The Compiler is deeply grateful to the many firms and individuals 
who provided advice and data for this book. 

The most recent sources in a very wide field have been con- 
sulted and it would be impossible to acknowledge them all 
individually. 

However, he would like to thank the following publishers for 
permission to use their tables either in full or in amended form: 

Oliver & Boyd Ltd. Physical and Mathematical Tables. 

(Clark). 
Macmillan & Company Ltd. Five-Figure Logarithms and 

Other Tables. (Frank Castle). 
Cambridge University Press. Four-Figure Tables. (Godfrey 

and Siddons). 
Elliott Process Automation Ltd. Relative Humidity Tables. 

He would also like to thank Mr B. D. Oakley, A.M.i.Mech.B., 
Mr R. E. Hack, f.p.s., m.r.s.u., and;Mr W. E. Clarke, l.r.i.c, 
m.r.s.h., for their help and advice. 



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tnv%»n«rnrt ^^'i-rt t^t^V Tf**^rr*iro 



INrifS fN — ——— — — — — _ _ — — OO OOOOO 

030000 oooooooop- t-r-i— e-i- r-r- 1- i-t- r— r-r-r-r— 
^Vt *t*t-<T*t*t •»<fr-**t^ Tj-^t^tmro nrt^wn 



r-»0"T — o 
— *no?\f*i*o 



Ol-M^M 
v-nrt«n%o»o 



o-3-«^i-*o 

I— <N I- (NI- 
OO r-i •*-» c?v r* 
voi— r— i— oo 



OAOXON OSO\C7\00\ 0\9«0>0\0\ 0\0>0>C7sO\ 



-"OOnvO 
ooope>o\CA 



— MM 



■*MOI-«n 
— wtOMO 

oSt7\ oS o\oS 



<NO V» — I— 
*n<o»rtvO\o 



■*oopo»o 

f> oo tJ- oo •*! 
co — >o oo M 
%OC-t- l-OO 



OiN — OOrO 

»noo\m 

viO\<NuiC7\ 

0O OO C7« O 0\ 



C7\0>e7*0SO\ 0\C7\C7»OC?\ 0\0\0\C7*0 



m\oo 

**ifN — 
C7*f^r— 
— MM 



r; l w-i wt — v% 



0«*OMM 
oow-i — 00 'V 
o>«-vr— Q"* 



Of) »/■»■*-— 
Ot'OClO 
I-— V-iOOM 
Ol— I— C— CO 



C>0\C7> 0\G*\C7\00\ 0\C7iO\0\0\ C7»C7»Cf\OCO 



ooor-*AQ 

*f OOINsCO 
OpOOO>C7\C7\ 

ChC*c\cj\o\ 



»tt-l- 

OOOI- 

238 



r«1 1— I— •»* OO 



\o — i— — \o 
I— — ^too — 
\or— r— i— oo 



OtOC\ O\O\O\O\0\ 0\C7*0\Ot> 00\OOC7\ 



•oooco 

DOM O 

— MM 
0%0>0 



v^0>O 

— OO 
M r: -v. 

— MM 



■0 000*0 — 

NOMOV 

o oo oo 



M — l-OO 

— co-r — r— 

^*n«o*o*o 

o oo oo 



l— MmtriM 

MOO r-k00r% 
I-O-TI— — 
*OI— I— I— 00 

ooooo 



r-OOl— r<1 
i— — «o\n 

-*00 — *J-CO 

opopooo 
ooooo 



>oo — o«*i 

ooi-wiMO 

- ■. r>, I ■- ~ K , 



w-ifOm^t 
f— -rT — t— f. 



ooo ooooo ooooo 



•OOO 

r-i-o 

I- — VI 

— MM 



ooMm— \o 



oor-«rr-oo 
**■, o I— r*\ O 
OOMtOOM 

^■ir»«o«n'0 



•r. — ^ — o 
OO^I— O 
*o I— I- l-OO 



00 — MO^O 

vr-otr- 
oo ooooo 



ooo ooooo ooooo ooooo ooooo 



sCO- 
rn roM 
I— — *rt 
— MM 



ooooo 
o v»r— %o-^ 

r— <rtm<->0 

co M vO O rn 
Mrncp'*'* 
OOO OOOOO 



r- — n 

Or— mO'O 
oo — v»cj\M 
tt«o»ow-i\o 



oooooo 

MC-MCOiN 

\oomvoo 
voxor— i-oo 



ooooo ooooo ooooo 



OO » 



mOOM 

r- — vioom 
OOOOO 



OOTOTfO 
w-iOMOO 

\oor-r-i— 



fi 00 M O O 

OO OOOOO 



ooooo ooooo 



I— Mr-i 

OOT 
— MM 



Mr— ooo ** 
m — oi— vi 
comv> 0«*» 
Mmmro^ 



l— I— Tf OOO 
M O >o M O 
t— OtTOO-h 
*T*r> </tw>vo 



OOO OOOOO OOOOO 



OVIOOO 

TO/l-V) 

•n o M vo o 
vo«or-t— i— 

ooooo 



v, oo o o *o 

OTONO 

coopopoo 
ooooo 



i-cr-ooo OHNCif 
JXCO00OO ooooo 



OS 

*o 
in 

T 



— ■^■^■ — so 

— tnofn *0 
v-ioo — w-ioo . soj 
opopooo ' 
OOOOO 



300 M «0 O 

opopooo ^^ 
ooooo I 



M 



r- — ioo\m 
roi— Or"*!— 

00 00 OOO 



M 



100 



101 



THE METRIC SYSTEM 



CONVERSION TABLES 



MEASURES OF LENGTH 



10 millimetres = 1 centimetre 
10 centimetres = 1 decimetre 
10 decimetres = 1 metre 
10 metres = 1 decametre 



10 decametres = 1 hectometre 
10 hectometres = 1 kilometre 
10 kilometres = 1 myriamctre 



MEASURES OF CAPACITY 



10 millilitres = 1 centilitre 
10 centilitres — 1 decilitre 
10 decilitres = 1 litre 



10 litres = 1 decalitre 

10 decalitres ■ 1 hectolitre 
10 hectolitres = 1 kilolitre 



1 litre = 1 cubic decimetre; I kilolitre = 1 cubic metre 
MEASURES OF WEIGHT 






10 milligrammes 
10 centigrammes 
10 decigrammes 
10 grammes 
10 decagrammes 
10 hectogrammes 
10 kilogrammes 
10 myriagrammes 
10 quintals 



— 1 centigramme 
= 1 decigramme 
= 1 gramme 
= 1 decagramme 
= 1 hectogramme 
= 1 kilogramme 
■ I myriagramme 
= 1 quintal 
= 1 millier or tonne 



MEASURES OF SURFACE 



100 square millimetres = 
100 square centimetres -■■ 
100 square decimetres = 
100 square metres — 

100 square decametres = 
100 square hectometres = 



1 square centimetre 

1 square decimetre 

1 square metre 

1 square decamotrc - 1 are 

1 square hectometre 

1 square kilometre 



In the following conversion factors the pound (or gram) 
is a unit of mass. Where the pound (or gram) is meant as 
a unit of force the term 'pound weight' (or 'gram weight') is 
used. 

All factors involving the change from the absolute to the 
gravitational system of units are based on the international 
standard acceleration due to gravity: 

g, - 32-1740 ft./sec. 2 - 980-665 cm./sec. 2 

The dimensions of all quantities are given in terms of the 
fundamental quantities: mass (M), length (L), time (T). 



7-92 inches = 1 link 
12 inches — 1 foot 
3 feet =1 yard 
6 feet » 1 fathom 



LENGTH (L) 

5i yards 

4 poles 

10 chains 



8 furlongs = 1 mile 



= I rod, pole or perch 
I chain 
1 furlong 



1 chain = 22 yards = 100 links 

1 mile = 80 chains = 1760 yards = 5280 feet 

1 nautical mile - 1-151 miles 6080 feet 



1 inch ■ 25-40 millimetres 
1 foot = 30-48 centimetres 
1 yard = 0-9144 metre 
1 chain ■■ 20- 12 metres 
1 mile = 1-609 kilometres 



1 millimetre = 003937 inch 
1 centimetre = 003281 foot 
1 metre - 39-37 inches 

1 metre — 1 -094 yards 

1 kilometre = 0-6214 mile 



1 nautical mile ■■ 1-853 kilometres 
1 fathom — 1-8288 metres 



10 centiarcs = 1 deciare 
10 deciares = 1 are 



10 ares = 1 decare 
10 decares = 1 rjectare 



CUBIC MEASURE 

1000 cubic millimetres = 1 cubic centimetre 
1000 cubic centimetres = 1 cubic decimetre 
1000 cubic decimetres = 1 cubic metre 



102 



183 






CONVERSION TABLES {continued) 

VOLUME (£.') 

4 plls = 1 pint 4 quarts = 1 j mp . gallon 

2 pmts = 1 quart 6-299 Imp. gallons = 1 cu. foot 

1 cu. foot = 1,728 cu. inches = 0-7787 bushel 

I cu. yard = 46,656 cu. inches = 21 03 bushels 

I shipping ton = 40 cu. feet of merchandise 

I shipping ton = 42 cu. feet of timber 

1 standard of timber= 165 cu. feet 

! J?£ enal sailoa = 277 ' 4 cu. u'chcs = 01605 cu. foot 
1 U.S. gallon = 2310 cu. inches = 01337 cu. foot 

1 "to* = 61 02 cu. inches = 003532 cu. foot 



CONVERSION TABLES (continued) 



MASS (JW) 
(All English units are Avoirdupois) 



1 cu. inch i 

1 cu. foot . 

1 cu. yard 

1 pint . 

1 Imperial gallon 

1 cu. foot 

1 Imperial gallon ■ 

1 cu. cm. 

1 cu." metre ■ 

1 cu. metre « 

1 litre 

1 litre 

1 litre 

I U.S. gallon 



= 16-39 cu. cms. 

■ 002832 cu. metre 
- 0-7646 cu. metre 

■ 0-5683 litre 
= 4-546 litres 

■ 28-32 litres 

■ 1-201 U.S. gallons 

■ 006102 cu. inch 

■ 35-32 cu. feet 

' 1 -308 cu. yards 
■■ I-OOOcu. cm. 

0-2200 Imperial gallon 
■■ 03532 cu. foot 
0-8327 Imperial gallon 



27-34 grains 
16 drams 
16 ounces 
7000 grains 
14 pounds 

1 grain 
1 dram 
1 ounce 
1 pound 
1 cwt. 
1 ton 



1 dram 
1 ounce 
1 pound 
1 pound 
1 stone 

00648 gram 

1-772 grams 
28-35 grams 

0-4536 kilograms 
50-80 kilograms 

1-016 tonnes 



28 pounds = 1 quarter 
4 quarters = 1 cwt. 
20 cwt. = 1 ton 
112 pounds = 1 cwt. 
2240 pounds = 1 ton 

1 milligram =s 001 543 grain 
1 gram = 15-43 grains 
1 gram = 003527 ounce 
1 kilogram = 2-205 pounds 
1 kilogram = 0-01968 cwt. 
1 tonne = 0-9842 ton 



1 tonne (metric ton) = 10 quintals = 1000 kilograms 
1 U.S. long ton = 2240 pounds = 1 English ton 
1 U.S. short ton = 2000 pounds --= 0-8929 English ton 
1 U.S. kip = 1000 pounds = 0-4465 English ton 

1 U.S. cwt. = 100 pounds = 0-8929 English cwt 



LINEAR VELOCITY (Jj) 



1 m.p.h. 
1 m.p.h. 
1 m.p.h. 



= 88 feet/min. 
= 1-467 feet/sec. 
= 0-4470 metre/sec. 



AREA (L') 

144 sq. inches = 1 sq. foot 4840 sq. yards = 1 acre 

9 sq. feet = 1 sq. yard 640 acres = 1 sq. mile 

I acre = I0gq. chains = 160 sq. rods = 43,560 sq. feet = 100,000 sq. links 

1 square of flooring or roofing = 100 sq. feet 



1 foot/min. = 0-5080 cm./sec. 



1 foot/min. = 001136 m.p.h. 
1 foot/sec. = 0-6817 m.p.h. 
1 metre/sec. = 2-237 m.p.h. 
1 cm./sec. = 1-967 feet/min. 



1 sq. inch 
1 sq. foot 
1 sq. yard 
1 acre 
1 sq. mile 
1 sq. centimetre 
1 sq. metre ■ 
1 sq. metre ■ 
1 hectare < 

1 hectare . 



6-452 sq. centimetres 
9290 sq. centimetres 

0-8361 sq. metre 
40-47 ares 
2590 hectares 

0-1550 sq. inch 
10-76 sq. feet 

1196 sq. yards 

2-471 acres 

0003861 sq. mile 



DENSITY 

1 lb./cu. in. ' 

1 lb./cu. ft. 

1 lb./cu. yd. 

1 ton/cu. yd. ■ 

1 grain/gal. 

I part/ 100,000 

1 part/million (p.p.m.) i 

1 g./cu. cm. ■ 

1 kg./cu. m. ■ 

1 kg./cu. m. ■ 

1 tonne/cu. m. i 

1 g./litre 

1 grain/gal. ■ 

1 grain/gal. > 



27-68 g./cu. cm. 
1602 kg./cu. m. 
0-5930 kg./cu. m. 
1-328 tonnes/cu. m 
001425 g./litre 
0-7017 grain/gal. 

i 007017 grain/gal. 

i 0-03613 lb./cu. in. 
006243 lb./cu. ft. 

i 1-686 lb./cu. yd. 

i 0-7532 ton/cu. yd. 

• 70-17 grains/gal. 

i 1-425 parts/100,000 

1 14-25 parts/million 



1 hectare = 100 ares = 10,000 sq. metres 



104 



105 



i 



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co 

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so -*t 
f> © m •«*■ en 

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ov oo 

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no £ ri o — 6 6 

r- r- o 



v-i vo 
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— vo 

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m — vn 

IN C* 00 

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vn vr> 

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en 

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I 



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1 

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g 


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5 

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| 


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| 


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9 


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g 




g 


1- 


6 


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1 


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'_ 




fl 


a 
5 


si 


H 


■ » 


-c 


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£ 


rj 


£ 


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co 


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n ov « « 

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vp vp oo J2 

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CONVERSION TABLES (continued) 



108 






DECIMAL EQUIVALENTS OF 


FRACTIONS 


A 01563 


ii 


•34375 


t* 


•67188 


A -03125 


H 


•35938 


H 


■6875 


A 0468* 


i 


•375 


H 


•70313 


A -0625 


H 


•39063 


U 


•71875 


& 07813 


H 


•40625 


ii 


•73438 


A -09375 


» 


•42188 


I 


•75 


A -10938 


A 


■4375 


« 


■76563 


i 125 


» 


■45313 


ii 


•78125 


A -14063 


« 


•46875 


H 


•79688 


A 15625 


h 


■48438 


ii 


•8125 


ii -17188 


i 


•5 


ii 


■82813 


A 1875 


it 


•51563 


a 


•84375 


tt -20313 


H 


•53125 


a 


•85938 


A 21875 


H 


•54688 


i 


•875 


Ji -23438 


A 


•5625 


H 


•89063 


i « 


H 


•57813 


if 


•90625 


Ji -26563 


ii 


•59375 


H 


•92188 


A -28125 


a 


•60938 


ii 


■9375 


« -29688 


i 


•625 


ii 


•95313 


A -3125 


H 


•64063 


ii 


•96875 


H -32813 


H 


-65625 


ii 


•98438 



1W 



DECIMALS OF A FOOT FOR 






EACH ViND OF AN INCH 





Inch 





1 


2 


3 


4 


S 






Inch 


6 


7 


8 


9 


10 


11 







00 


00833 


01667 


0-2500 


0-3333 


0-4167 





0-5000 


0-5833 


0-6667 


0-7500 


0-8333 


0-9167 




A 

A 
A 

i 


•0026 
•0052 
•0078 
•0104 


•0859 
•0885 
•0911 
■0938 


•1693 
•1719 
•1745 
•1771 


•2526 
•2552 
•2578 
•2604 


■3359 
•3385 
•3411 
•3438 


•4193 
•4219 
•4245 
•4271 






A 
A 
A 
i 


•5026 
•5052 
•5078 
•5104 


•5859 
•5885 
•5911 
•5938 


•6693 
•6719 
•6745 
•6771 


•7526 
•7552 
•7578 
•7604 


•8359 
•8385 
•8411 
•8438 


•9193 
■9219 
•9245 
•9271 




A 

A 
A 
i 


•0130 
•0156 
•0182 
•0208 


■0964 
•0990 
•1016 
■1042 


•1797 
•1823 
•1849 
•1875 


•2630 
■2656 
•2682 
•2708 


■3464 
•3490 
•3516 
■3542 


•4297 
■4323 
■4349 
■4375 






A 

A 
A 
i 


•5130 
•5156 
•5182 
•5208 


•5964 
■5990 
•6016 
•6042 


•6797 
•6823 
•6849 
•6875 


•7630 
•7656 
•7682 
•7708 


•8464 
•8490 
•8516 
•8542 


•9297 
■9323 
•9349 
•9375 




A 
A 
ii 

i 


•0234 
•0260 
•0286 
•0313 


•1068 
•1094 
•1120 
•1146 


•1901 
•1927 
•1953 
•1979 


•2734 
•2760 
•2786 
■2813 


■3568 
•3594 
•3620 
•3646 


•4401 
■4427 
•4453 
•4479 






A 
A 

ii 

i 


•5234 
•5260 
•5286 
•5313 


•6068 
•6094 
•6120 
•6146 


•6901 
•6927 
■6953 
•6979 


•7734 
•7760 
•7786 
•7813 


•8568 
•8594 
•8620 
•8646 


•9401 
•9427 
•9453 
■9479 




a 

A 
ii 
i 


•0339 
•0365 
•0391 
0417 


•1172 
•1198 
•1224 
•1250 


•2005 
•2031 
•2057 
•2083 


•2839 
•2865 
•2891 
•2917 


•3672 
•3698 
•3724 
•3750 


•4505 
•4531 
•4557 
•4583 






ii 

A 
ii 
i 


•5339 
•5365 
•5391 
•5417 


•6172 
■6198 
•6224 
•6250 


■7005 
•7031 
•7057 
•7083 


■7839 
•7865 
•7891 
•7917 


•8672 
■8698 
•8724 
•8750 


•9505 
•9531 
•9557 
•9583 




a 

A 


•0443 
■0469 
■0495 
•0521 


•1276 
•1302 
•1328 
•1354 


•2109 
•2135 
•2161 
•2188 


•2943 
•2969 
•2995 
•3021 


•3776 
■3802 
■3828 
•3854 


•4609 
•4635 
•4661 
•4688 






ii 
A 
ii 

i 


■5443 
•5469 
•5495 
•5521 


•6276 
•6302 
■6328 
■6354 


•7109 
•7135 
•7161 
•7188 


•7943 
•7969 
•7995 
■8021 


•8776 
•8802 
•8828 
■8854 


•9609 
•9635 
•9661 
•9688 




u 

H 


•0547 
•0573 
•0599 
0625 


•1380 
•1406 
•1432 
•1458 


•2214 
•2240 
•2266 
•2292 


•3047 
•3073 
•3099 
•3125 


•3880 
•3906 
•3932 
•3958 


■4714 
•4740 
•4766 
•4792 






ii 

J 


•5547 
•5573 
•5599 
•5625 


■6380 
■6406 
•6432 
•6458 


•7214 
•7240 
•7266 
•7292 


■8047 
■8073 
•8099 
■8125 


•8880 
•8906 
•8932 
■8958 


■9714 
•9740 
•9766 
•9792 




ii 

i 


0651 
0677 
■0703 
•0729 


•1484 
•1510 
•1536 
•1563 


•2318 
•2344 | 
•2370 1 
•2396 ' 


■3151 
•3177 
•3203 
•3229 


•3984 
•4010 
•4036 
•4063 


•4818 
•4844 
•4870 
•4896 






ii 

a 

si 

i 


•5651 
•5677 
■5703 
■5729 


•6484 
•6510 
•6536 
•6563 


•7318 
•7344 
•7370 
•7396 


•8151 
•8177 
•8203 
•8229 


•8984 
■9010 
■9036 
•9063 


•9818 
■9844 
■9870 
•9896 


*< 


ii 

i 


•0755 
0781 
0807 


•1589 
•1615 
•1641 


•2422 
•2448 
•2474 


•3255 
•3281 
•3307 


■4089 
■4115 

•4141 


•4922 
■4948 
■4974 






ii 
H 
ii 
i 


•5755 
•5781 
•5807 


•6589 
•6615 
•6641 


•7422 
•7448 
•7474 


■8255 
•8281 
■8307 


■9089 
•9115 
•9141 


•9922 
•9948 
•9974 

10000 J 


<tf * 


« 






110 














111 








w 





t w 



TEMPERATURE CONVERSION CHART 

C = Centigrade F = Fahrenheit 



* 





c 


F 




c 


F 




c 


F 


3S0- 


F~ 


r— ; 


480- 


t~~7 


1 — 


580- 


1 — 


r— 






















= 710- 






= 890- 






= W70- 






™ 


-~ 




~~ 


— 






— . 






































370- 


— 700- 


E 


470- 


E880- 


E 


570- 


E1060 


= 




~ 


«■ 




~ 


— 




— 


— 




= 690- 






E 870- 






— 1050- 


~ 




— 


— 




mm 


__ 




... 






















360- 


E 680- 


EE 


460- 


= 860- 


"~ 


560- 


= 1040- 


) 








































{= 670- 


~~ 




E 850- 


= 




E 1030- 






















350-] 


E 660- 


j; 


450- 


E840- 


E 


550- 


E 1020- 


EE 
























— 






— 






— 




E 650- 


H 




E 830- 


zn 




E1010- 


7~Z 


340 




5 


440i 




E 


540- 








E 640- 


™ 




E 820- 


— 




E 1000- 








*■■ 






— 






— 






















= 630- 


™" 




= 810- 


^ 




E 990- 


— ] 


330- 




^ 


430- 




E 


530- 








E 620- 


E 




E 800- 


-— 




E 98°- 








—~ 




E 


— 




E 




320- 


E 610- 




420- 


5 790- 


— 


520- 


S 970- 
























E 600- 






E 780 -, 






E 960- 






















310- 


= 590- 




410- 


E 770- 




510- 


E 950- 


= 
























— • 












, 




= 580- 


*^^ 




= 760- 






E 940- 


~ 






































300- 


E 670- 


3 


400- 


= 750- 




500- 


E 930- 


= 


























































E 560- 


£3 




E 740- 






E 920- 




290- 




— 


390- 






490- 








E 550- 






E 730- 






E 910- 






































E 540- 






E 720- 






E 900- 




280-1 






380- 






480-1 





112 



TEMPERATURE CONVERSION CHART 

C = Centigrade F = Fahrenheit 

C F C F C F 

80-r-= p— 180-pr cz 280-p: p: 



= 170 



70- E 160 ' E 170- E 34 °" E 270- 3 K0 " E 



60- = 140- E 160- = 320- — 260- =; 500- — 



"S 130 
»■! CO 



= 110 



ZD 



2 o 



H 



150 



= 150 



40- - 

— ioo4— : 



140 



-10 



E s3 ' 

E 80 

E 70 ' 

■ 60 
50 

E *° 

E 30 

E 20 

E io 



~ 

-20= -4 



r: 350- — =: 530- — 



350 



E 310 

E 300-E 

E 290 

E 280 



= 250 



= 270 
130- E 

— 2604— 



— 250 
120 - 



= 240 
280 

|= 220 



— no = 230-=; 210-=: 



100- = 2io- = 



80 



— 90= ~ 190 



= 203 = 
E 190 E 
E 180- 



113 



= 490 
E 480 



= 470 
240- E 



— 230 



— . 220 = 



200 



— 180 



510 



460- 
£ 450- E 
E 440- 
E 430- 

420- 

410- 
|= 400- 
E 390- 
E 380-I 
E 370- E 

E 360- E: 



4 






- 

CO 

< 

H 

z 

o 

— 

o: 

Id 

> 

o 

u 

a 

as 

CO 

CO 

Id 
OS 

0. 



» 







S 


IN 


VN 


l~ 


o\ 


CN 


T 


so 


ov 


— CI 




at 




O 


CN 


■fl- 


>o 


CN 




CI 


vo 


CO p 




o 




cn 


>-- 


(■4 


vo 


on 


CO 


OO 


CN 


vo 


Q V> 








mm 


CN 


^- 


VI 


vo 


00 


Ov 




CN 






















mm 










CO 

en 


8 


CO 

oo 


vo 

c 


r- 
CN 


o 

CO 


CN 


3; 


r> 


ON — 
d so 






— 


*o 


ON 


Tf 


00 


CN 


vo 


o 


a 


0\ r*l 








« 


CN 


CO 


<o 


VO 


oo 


ov 




ro vn 






















*■! 










so 


CO 


9 


CO 


•o 


r- 


o 


CN 


••* 


r* on 




r- 




on 


*■* 


vo 


00 


o 


CO 


vn 


f~ 


ON — 




o 




o\ 


•*!• 


00 


IS 


VO 


_ 


•O 


s 


CO 


t*- IN 










cn 


CO 


vn 


vo 


00 


Ov 


CN 


c» w-i 






















^N 








* 




R 


JS 


9S 

OV 


s 


CO 

1- 


8 


OO 


o 


CN 
CO 


vn r^ 




© 




00 


a 


VO 


— 


VO 


Ov 


CO 


CO 


<N 


so o 










co 


v> 


vo 


t- 


c\ 


o 


CN 


m IO 






if 
















" 


"■* 


f^ — 




























« 


1 2 


s 


no 
vo 


{5 


o 


a 


3 


5S 


s 


CN ■<* 




o 


quare 

1 7 " 


CN 


vo 

co 


5 


3 


oo 
r- 


S 


SO 

o 


§ 


VN ON 

2 2 




























t/a 






















•f 


« S 


5\ 


I- 


NO 
CO 


00 

vo 


00 


o 


a 


00 


O CN 

r* on 




o 


f 


fa V, 


on 


■* 


OO 


CN 


VO 


— t 


vo 


ON 


c> r» 






■l 




CO 


■N* 


vo 


1- 


on 


o 




CI it 






•o 
















»■• 








1 


■ ■ 
























f- 


C\ 


-* 


3 


vo 


oo 




CO 


vn 


00 o 




**) 




CN 


Tf 


r*- 


*■ ' 


CO 


VO 


00 


© 


CN VN 




o 




-a- 


00 


CN 


vo 


«-( 


vn 


c\ 


CO 


oo 


IN SO 












CO 


•«r 


vo 


r~ 


CO 


o 


mm 


Cl Tj" 






in 


r- 


On 


IN 


■* 


VO 


On 




CN 


VN 00 




M 




00 


o 


CN 


vo 


r- 


c\ 




■* 


so 


CO o 




o 




CN 


r— 


-^ 


vo 


o\ 


CO 


CO 


CN 


so 


O VN 












CO 


n- 


VO 


r» 


CO 


o 


mm 


ci *r 






CN 


vn 


r- 


o\ 


<-i 


t 


SO 


a 




c> so 




mt 




^t 


SO 


oo 


o 


CO 


VO 


r- 


CN 


-*■ so 




6 






VN 


on 
n 


3 


00 


CN 


so 

CO 


8 


VN 


a ? 






s 


cn 


vo 


r> 

vo 


OV 

00 


cn 


s 


VO 

vo 


ON 


s a 




o 




o 


*■ 


00 


f-J 


VO 


M 


vn 


§5 


en 


00 CN 












CN 


t 


vo 


r- 


CO 




CN V? 
























*^ 


•^ w+ 




is 


J 

r 


© 


*H 


N 


CO 


V 


tf) 


SO 


r> 


00 


0\ O 





.114 



VISCOSITY CONVERSION TABLE 



Seconds 


Seconds 


Degrees 

Lnglcr 


Kinematic 




Redwood 
No. 1 


Savboll 
Universal 


Viscosity 
Stokes 




30 


33 


106 


0015 




40 


45 


1-45 


0058 




60 


68 


2-08 


0126 




80 


91 


2-73 


0185 




100 


114 


3-37 


0-237 




150 


170 


4-91 


0-365 




200 


226 


6-51 


0-487 




220 


248 


7-15 


0-532 




250 


283 


815 


0-617 




300 


340 


9-78 


0-741 




350 


397 


114 


0-865 




400 


452 


130 


0-988 




450 


508 


14-7 


Ml 




500 


564 


16-3 


1-23 




600 


676 


19-5 


1-48 




700 


790 


22-8 


1-73 




800 


902 


261 


1 97 




900 


1015 


29-3 


2-22 




950 


1068 


30-9 


2-34 




1000 


1130 


32-6 


2-47 




1100 


1242 


35-9 


2-71 




1200 


1354 


391 


2-96 




]300 


1467 


42-4 


3-21 




1400 


1576 


45-7 


3-46 




1500 


1690 


48-9 


3-70 




1600 


1804 


51-2 


3-95 




1700 


1914 


55-4 


4-20 




1800 


2028 


58-7 


4-45 




1900 


2144 


620 


4-70 




2000 


2255 


65-2 


4-94 




2200 


2478 


71-8 


5-43 




2400 


2696 


78-2 


5-93 




2600 


2924 


84-8 


6-42 




2800 


3142 


91-3 


6-92 




3000 


3370 


97-8 


7-41 




3250 


3650 


105-9 


803 




3500 


3935 


1141 


8-65 




3750 


4220 


122-2 


9-26 




4000 


4500 


130-2 


9-88 




4500 


5060 


146-6 


1111 




5000 


5620 


1630 


12-34 





115 




SPEEDS OF FLOW OF WATER 



MATERIAL DENSITIES 



Pipe 
Bore 
ucnei 




Velocity in Feci per Second 






2 


4 


< 


8 


10 








Gallons per Hour 






i 


15 


30 


46 


61 


76 




J 


34 


69 


103 


137 


172 




i 


61 


122 


184 


245 


306 




1 


94 


190 


285 


380 


474 




i 


138 


276 


414 


552 


690 




1 


245 


490 


735 


980 


1225 




n 


382 


765 


1150 


1530 


1910 




ii 


550 


1100 


1650 


2200 


2750 




2 


980 


1960 


2940 


3920 


4900 




2} 


1530 


3060 


4590 


6120 


7650 




3 


2200 


4410 


6620 


8820 


11000 




4 


3920 


7840 


11750 


15700 


19600 




5 


6120 


12250 


18350 


24500 


30600 




6 


8800 


17600 


26400 


35200 


44000 




7 


12000 


24000 


36000 


48000 


60000 








Pounds per 


Cubic feet 


Cubic inches 


Material 


cubic Toot 


per too 


per pound 


Fresh water 


62 


36 


28 


Sea water 


64 


35 


27 


Resin 


66 


34 


26 


Ground dry fireclay! 

Saltcakc J 

Bones 

Nitrate of ammonia V 


70 


32 


24-6 


72 


31 


24 


Nitrate of soda J 








Chalk lumps\ 
Loose earth / 


78 


29 


22 


Calcined limestone "| 










Crushed chalk 










Earth 

Loose clay and marl 


■ 


80 


28 


21-6 


Crushed slag 










Ground gypsum 










Phosphate rock 


81 


27-5 


21 


Blast furnace slag"| 








Crushed silica > 


86 


26 


20 


Portland cement J 








Shingle 


88 


25-5 


19-5 


Broken limestone"! 
Coprolites / 


90 


25 


19-3 








Clay shale, loose 


93 


24 


18-5 


Dried mud "1 








Stone dust > 


95 


236 


18-2 


Granite chippingsj 








Fine sand 


96 


23-2 


17-9 


Coarse graven 
Plaster / 


98 


23 


17-7 


Cement clinker -. 








Coarse pit sand 










Common bricks 










Crushed basalt 


> 


100 


22-4 


17-2 


Pit dirt 










Phosphate pebble 










Slate dust ' 








Hard bath stone, broken 


102 


22 


17 


Plaster of Paris'! 
Lead ore / 


106 


21 


16-2 


Gravel, average 


109 


20-5 


16 


Bauxite \ 
Phosphate meal/ 


110 


20-4 


15-7 



116 



117 



MATERIAL DENSITIES (continued) 



MATERIAL DENSITIES (continued) 




iniaM 


Pounds per 


Cubic reel 


Cubic inches 




cubic Tool 


per ton 


per pound 




Ballast, loose "| 










Powdered sulphur > 


112 


20 


15-4 




Tin ore J 










Asphalt, loose "1 










Ground cement I 










Concrete 


120 


18-7 


14-5 




Gypsum, brokenJ 










Bath stone 1 










Solid chalk [ 


125 


18 


14 




Solid rock sulphurj 






* ■ 




Barytes ") 










Red sandstone > 


130 


17 


13 




Powdered phosphatej 










Derby stone, brokcn\ 
Salt rock / 


136 


16-5 


12-7 




Plumbago "1 










Portland stone, broken I 










Sandstone, broken 


140 


16 


12-5 




Quartz, broken J 










Granite, broken \ 
Spanish iron ore/ 


150 


15 


11-5 




Iron pyrites 


156 


14-3 


10-6 




Shale \ 
Zinc spelter/ 


162 


13-8 


10-5 




Crushed dolomite 


165 


13-5 


10-4 




Quartz sand 


170 


13 


10-2 




Lead oxide 


184 


12-2 


9-4 




Copper pyrites, fine 


187 


12 


96 




Iron ore, Clydesdale 


190 


11-8 


9-5 




Tin ore 


200 


1 1-2 


8-2 




Brown iron ore 


245 


9-2 


71 




Red iron ore 


320 


7 


5-4 




Dry hops 


6-5 


350 


270 




Cork dust 


7 


320 


246 




Dry sawdust 


8 


280 


216 




Wood meal 


8-5 


270 


208 




Bran \ 
Dry Peat/ 


11 


204 


157 




Beet, dried pulp 


14 


160 


125 




Flaked soap 


16 


140 


108 




Ground oak bark 


17 


132 


102 




Logwood dusfi 
Flue dust / 


18 


124 


95 







Pounds per 


Cubic feet 


Cubic inches 




Material 


cubic root 


per ton 


per pound 




Dry paper pulp\ 
Green malt / 


20 


112 


86 




Cotton seed 


22 


100 


77 




Breadcrumbs -i 










Charcoal 1 


23 


97 


75 




Locust beans f 










Calcined bones J 










Degreased crushed bones 


25 


90 


69 




Sccdlac \ 
Spent tan/ 


27 


83 


64 




Shredded soap\ 
Wood chips / 


28 


80 


61-5 




Damp wood pulp i 












Dry apple pulp or pumice 










Gas coke 


■ 


30 


75 


58 




Malt 












Oats 












Hcmpsecd 


31 


72 


55 




Crushed bones"| 










Hydrated lime > 


35 


64 


49 




Soda ash J 










Cotton seed"! 










Rape seed > 


36 


62 


47 




Spent hops J 










Buckwheat 


37 


61 


46 




Sugar beet 


38 


59 


45 




Coke breeze *) 










Barley I 


39 


58 


44-5 




Hot wet grains | 










Oatmeal 










Furnace coke "^ 










Gasworks lime > 


40 


56 


43 




Steamed bonesj 










Indian com mean 










Linseed > 


41 


55 


42 




Rye ) 










Bean and pea meal") 










Flour >■ 


43 


52 


40 




Coal nuts J 










Coal ashes 44 


51 


39 





118 



119 




MATERIAL DENSITIES (continued) 





Pounds per 


Cubic feet 


Cubic inches 




Material 


cubic Toot 


per Ion 


per pound 




Anthracene •> 










Powdered coal 










Indian com or maize > 


45 


50 


38-5 




Coarse salt 










Soda ash J 










Sodium bicarbonate 


46 


49 


37-7 




Potatoes! 










Wheat / 


47 


48 


37 




Horse beans 


49 


46 


35-5 




Peas and beans -« 








Fine white sugar 










Broken ice \ 


50 


45 


34-6 




Sulphate of ammonia 1 










Wet char J 










Welsh steam coal ") 










Anthracite coal, loose I 










Quicklime ( 


53 


42 


32-5 




Rye J 










Bone meal "1 












Block ice 












Boiler ashes 


' 


56 


40 


31 




Asbestos grit- 












Broken glass or cullet 










Crushed dolomite (calcined) 

Pilch 

Oxide of iron f 










60 


37 


28-5 




Wet bone char 










Superphosphate of lime 











RELATIVE HUMIDITY TABLES 

Relative Humidity 

Relative humidity is defined as the ratio, expressed as a 
percentage, between the water vapour in air at a given tem- 
perature and the maximum water vapour the air can hold 
(i.e. saturated air) at the same temperature. 

How to use the tables : 

Take the reading of the wet-bulb and dry-bulb tempera- 
tures at as nearly the same moment as possible. 

Subtract the wet-bulb reading from the dry-bulb 
reading. 

The per cent relative humidity is the number at the 
intersection of the temperature difference column (vertical) 
with the dry-bulb temperature column (horizontal). 




120 



121 





Is 

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ATOMIC WEIGHTS-PHYSICAL 
AND CHEMICAL SCALES 

Recently the Council of the International Union of Pure 
and Applied Chemistry iesolved that a scale of atomic 
weights based on the whole number 12, as the atomic weight 
of the dominant natural isotope of carbon, carbon 12, be 
adopted. 

In the tables which follow atomic weights are given based 
on carbon, as it occurs naturally, = 12. The difference be- 
tween the atomic weights quoted and those related to 
C 12 = 12 amounts to less than 43 parts per million. Natural 
carbon consists of two isotopes, C 12 and C 13 , of relative 
abundance 98-892% and 1-108%. The chemical basis for the 
atomic weights is thus an average value for the mixture. 
This is a valid basis for the table since the relative abundance 
of the two isotopes is practically constant. 

In physics it is the behaviour of individual atoms which is 
of importance, so an average value for their relative weight 
is not suitable. Consequently, for physical measurements, a 
new table of atomic weights has been produced based on the 
one isotope C 12 = 12000. To avoid confusion in terminology 
it is the modern practice to give the units of weight on this 
scale the name atomic mass unit (a.m.u.), e.g. C" = 12000 
a.m.u.; 1 a.m.u. - 1-6598 x 10~ 24 g. Mass spectrographs 
can determine the relative weights of individual isotopes 
with high accuracy. Knowing the relative abundance of the 
carbon isotopes, the average 'atomic weight' of naturally 
occurring carbon can be found. 



127 














THE PERIODIC 

giving atomic number, chemical symbol 




Group 1 


Group 2 


Group 3 


Groop 4 


Group 5 




A 


B 


A 


B 


A 


B 


A 


B 


A 


B 




1 

H 
1-0080 







— 


— 


— 


— 


— 


— 


— 




3 

U 

6-940 





4 

Be 

9013 


— 


S 

B 

10-81 


— 


6 

C 

12-00 


— 


7 

N 

14-007 


— 




II 

Na 
22-990 





12 
Ms 
24-31 


— 


13 

Al 

26-98 


— 


14 

SI 
28-09 


— 


15 
P 

30-974 


— 






19 
K 

39102 


~~ 


20 
Ca 

40-08 


— 


— 


21 

Sc 
44-956 


— 


22 
Tl 

47-90 


— 


23 
V 

50-94 




— 


29 
CD 

63-54 


— 


30 

Zn 
65-37 


31 

o» 

69 72 


— 


32 

Ge 

72-59 


— 1 33 
As 
74-92 


— 




37 
Rb 

85-47 




38 

Sr 

87-62 


" 


" 


39 
Y 

88-90 


" 


40 
Zr 

91-22 


" 


41 
Gk> 
MM 

92-91 




mm 


47 

107-170 




48 
Cd 

112-40 


49 

In 
114-82 


— 


SO 

Sn 
118-69 


— 


51 

Sb 

121-75 


— 




55 

Cs 

132-90 




56 

Ba 

137-34 






57 71 
lUro 
Bantu 

(•oe 




72 
Hf 

178-49 




73 

Ta 

180-95 


— 


79 

Au 
197-0 


— 


80 
200-59 


81 
Tl 

204-37 


— 


82 
Pb 

20719 


— 


83 

Bl 

208-98 


— 


87 

Fr 

P23| 




S8 

Km 

226135 






89-100 

Actinium 
Scries 

<K>0 

1% 






















128 





— Ma 


ss num 


twrof 



TABLE 

and atomic weight (C = 12-00) 



Group ( 


Group 7 


Group 8 


Group 


Electron 

Orbital 

No. 




A 


B 


A 


B 




— 


— 


— 


— 


— 


— 


— 


' 2 

He 
41)03 


2 




8 
O 

15999 


— 


9 

F 
19-000 


— 


— 


— 


— 


10 

Nc 
20-183 


2 
8 




16 

S 

32-064 


— 


17 

CI 
35-453 


— 


— 


— 


— 


18 

A. 

39948 


2 
8 
8 




— 


24 
Cr 

52-00 


— 


25 

Mn 
54 94 


2ft 

Fo 

55-85 


27 
Co 

58-93 


28 

NI 

58-71 




}« 




34 

So 

78-96 


~~^^^^ 


35 

Br 

79 909 


— 


— 


— 


"" 


36 
Kr 

83-80 




~" 


42 
Mo 
95-94 


~~ 


43 

Tc 
1991 


44 
Ru 
101-1 


45 

Rh 

102-90 


46 
Pd 

106-4 




ll 

IS 

J ! 




52 

To 

127-60 


— 


S3 
I 

126-90 


— 


— 


— 


— 


54 

Xe 

131-30 






74 
W 

183-85 




75 
Re 

186-20 


76 
Os 
190-2 


77 
lr 

192-2 


78 

Pt 

19509 




2 
8 

32 
18 

8 




84 
Po 

[210] 


— 


85 

At 
B101 


— 


■" 


— 


~ • 


86 

iln 
[2221 

























longest lived isotope 



129 



THE PERIODIC TABLE (continued) 



The Rare Earths 


Elcctroa 

Orbital 

No. 




57 
La 

138-91 


58 
Ce 

140-12 


59 
Pr 

140-91 


60 

Nd 

144-24 


2 
8 
18 
32 
9 
2 




61 
Pm 

1147] 


62 

Sm 
150-35 


63 
Eu 
152-0 


64 

Gd 

157-25 




65 
Tb 

158-92 


66 

Dy 
162-50 


67 

Ho 

164-93 


68 

Er 
167-26 




69 
Tm 

168-93 


70 

Vb 

17304 


71 

Lu 

174-97 


^ 





The Actinium Series 


Electro* 

Orbital 

No. 




89 
Ac 

227 


90 
Th 

23204 


91 

Pa 
£231] 


92 

U 
238-03 


2 
t 

It 

32 

T 

9 
2 




93 94 
Np Pn 
1237] [242] 


95 
Am 
1243] 


96 
Cm 
(247] 




97 

Bk 

[247] 


98 

Cf 

[249] 


99 

Es 
P54] 


100 
Fm 
[253] 




101 1 
Mv 

[256] 


102 

No 

1253] 


103 
Lw 

[257] 










130 



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INTERNATIONAL TEMPERATURE SCALE 1948 
as at April 1957 

SWS. WnSSRf ™*u$ d 3,m0SpheriC pressurc of «>«•» 



Primary Fixed Points 
Boiling point of oxygen 
Freezing point of water 
Boiling point of water 
Boiling point of sulphur 
Freezing point of silver 
Freezing point of gold 

Secondary Fixed Points 
Sublimation point of solid CO, 
Freezing point of mercury 
Triple point of water 

Transition point of sodium sulphate decahydrate 
I nple point of benzoic acid 
Boiling point of naphthalene 
Freezing point of tin 
Boiling point of benzophenonc 
Freezing point of cadmium 
Freezing point of lead 
Boiling point of mercury 
Freezing point of zinc 
Freezing point of antimony 
Freezing point of aluminium 
Freezing point of copper (in a reducing atmosphere) 
Freezing point of nickel wyiicny 

Freezing point of cobalt 
Freezing point of palladium 
Freezing point of platinum 
Freezing point of rhodium 
Freezing point of iridium 
Freezing point of wolfram (tungsten) 

Some Additional Important Temperatures 



•c. 

-182-970 

100 

444-600 
960-8 
10630 

°C. 

-78-5 

-38-87 
0-0100 
32-38 

122-36 

2180 

231-9 

305-9 

320-9 

327-3 

356-58 

419-5 

630-5 

6601 
1083 
1453 
1492 
1552 
1769 
1960 
2443 
3380 




Absolute zero q° k 

A point of helium 2-186" K 

Boiling point of helium 4-216* K." 

Freezing point of hydrogen 14°K. 

""oiling point of hydrogen 20-4° K, 

g point of nitrogen 63-3° K 

point of nitrogen 77-32° k! 

point of oxygen 54-8" K 



-273-15 ± -02° C* 

-259-2* C. 
-252-8* C. 
-209-9* C 
-1 95-8* C, 
-218-4* C. 



ly accepted value. In the U.S.A. the value -27316° C !« anA^^i . lm. 
cem work indicaies a value of -273-135 + 0015" r " tfared - whJo 



Estimated temperature of the sun's radiating layers 6< S?o £' 

Estimated temperature of the sun's core 2 x 10 K. 

Estimated temperature of the radiating layers of the o 

hottest stars 32,000 K. 

To convert degrees Celsius (centigrade) to degrees absolute add 27315. 



ATOMIC AND MOLECULAR CONSTANTS 

The electronic charge (e) = 4-803 x 10" 10 e.s.u. = 1-602 x 10-«* 

e.m.u. = 1-602 x 10- 1 " coulombs. 
Electronic mass (»»„) - 9108 x 10-» g. 

Specific electronic chargc(- e ) = 5-273 x 10"e.s.u./g. = 1-759 x 10' 

V"o/ 

c.m.u./g. - 1-759 x I0 8 coulomb/g. 
Mass of hydrogen atom (Mh) = 1-673 x 10"" g. 
Mass of proton (M p ) = 1-672 x 10"" g. 
Mass of neutron (M„) = 1-675 X 10"" g. 

MH = 18 3 7 M£ = 183 6. 

nto »'o 

Velocity of light (c) - 2-998 X 10"> cm./s. 

Boltzmann's constant (k) = 1-380 x 10-" erg/degree. 

Planck's constant (h) = 6-625 x 10-" erg second. 

fi = A = 1-054 x 10-" erg second. 
2w 

Rydberg constant (for nucleus of infinite mass) Rco = 2irm«eVi -*«-* 

<= 109737 cm.- 1 . , „__ , 

Rydberg constant (for hydrogen) (Rh) = 109677-6 cm. '. 
Volume of 1 gram-molecule (mole) of an ideal at N.T.P. = 22-41 5 litres 

(chem. scale). 

Fine structure constant - = 13704 

Calcite grating space, 20° C. (</,.) = 3036 x 10-' cm. 
Atomic radius ~10" 8 cm. Nuclear radius ~10-" cm. 



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MEAN RANGES IN AIR OF a-PARTICLES OF 
THE PRINCIPAL NATURAL B-EMITTERS 

(at 15° C. and 760 mm. Hg.) 



Th 


2-48 cm. 


u, 


270 cm. 


AcU 


i/2-9 cm. 
1308 „ 




RdTh 


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u„ 


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Pa 


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ThX 


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Io 


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Tn 


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Ra 


328 „ 


Ac 


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14-30 „ 




At"« 


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RaC 


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At" J 


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Po 


3-84 „ 


At«'» 
AcC 
AcC' 


4-9 „ 
5-42 „ 
6-53 „ 




Sm 1 " 


105 „ 






144 



TABLE OF ISOTOPES AND 

RELATIVE ABUNDANCE OF 

THE ELEMENTS 

The number of protons in a nucleus is usually designated 
by Z and is called the atomic number. Since the normal atom 
is electrically neutral, it must contain an equal number of 
planetary electrons. The chemical properties arc determined 
by the number and arrangement of the electrons and hence 
the atomic number decides the behaviour of a given atom, 
i.e. determines which clement it is. 

The number of neutrons in a nucleus is usually designated 
by N. The sum, N + Z, represents the total number of 
protons and neutrons in a nucleus and is known as the mass 
number, A. 

Atoms which have the same atomic number (i.e. exhibit 
identical chemical properties) but which have different mass 
numbers are called isotopes. 

In the following table the isotopes whose mass numbers are 
printed in bold-face type occur naturally and if they axe 
radioactive this is shown by an asterisk (*). All other isotopes 
are artificial and are radioactive. The percentage abundance 
of the natural isotopes is given in parenthesis after the 
appropriate mass number. 

Where no stable isotope of an element is known, the mass 
number of the longest-lived isotope in the atomic weight 
column is shown in brackets, e.g. Technetium [99]. 



145 




TABLE OF ISOTOPES {continued) 




Mass numbers of the isolopes 



1 (M-M5%), 2 (0 015% , 3 

6 (7-52";,). 7 (92-48%). 8, 9 

7, 8. 9 (100%). 10 

8^9, 10 (~l8-5%). U (-81-5%). 

i 'V,-/ 2 * 98892 ^- » (1-108%), 
'2. i3. 14(99-635%). IS (0-365%), 

17. 18. 19 (100%). 20, 21 

I 22 '(WnTO"' *' (0 ' 2S7%) - 

20, 21, 22, 23(100%), 24. 25 
24, 25 26. 27 ft 00%), 28, 29 
28. 29, 30. 31 (100%). 32. 33, 34 

3 ?24 3 6 3 % 3 , 4 -38 3 . S 39 (7S ' 4%> - * » 

3 39 3 40 ( ^|UI:4l (0 °" %) - 
"• ,3?. J? (9308%). 4«« (00119%), 

41 (6-911%). 42. 43, 44 
39 -.*> i 9 «' 9 '%). 41. <2 (0-64%). 
^/K 1 , 45 ""'- ** <*<>*%>. -15, 46 
(0-0033%). 47. 48 (6-185%), 49 

48 4*9 * 4 ' <S (,M%)> **• 47 - 

43 /.* 4 ;4 5, . 4< < 7 ' 9S %>, fi 0-7S%), 

nfHfaKV"* 

50. 51. 52. 54. 55 (100%). 56, 57 
TTO f 4 , IS"' i). 55. 56(91-68%), 
,57 (2-17%) 58 (0-31%). 5'.. 60 
3 -*., 5 5. 56 57. 58. S» (100%). 60, 
61, 62, 64 

5 ?k<V,l,? S < 6 7-76%>. 59, 60, 
2616%), 61 (1-25%), '62 

^27-t^^ «7 48 ^nV , 65 es« 

(36-74%), 75,76 (7®, 78 



TABLE OF ISOTOPES (continued) 



Alomic 
number 



33 
34 



37 
38 



40 

41 
42 

43 
44 

45 

46 



Element 



Arsenic 
Selenium 



35 Bromine 

36 Krypton 



Rubidium 
Strontium 



39 Yttrium 



2jrconium 



Columbium 1 
Niobium J 
Molybdenum 



Technetium 
Ruthenium 



Rhodium 
Palladium 



Symbol 



47 Silver 

48 Cadmium 



49 ! Indium 

50 Tin 



As 

Se 

Br 
Kr 

Rb 

Sr 

Y 

Zr 



Cb) 
NbJ 
Mo 



Tc 
Ru 

Rh 
Pd 

Ag 
Cd 

In 
So 



Alomic 

weight 

(C- 12-00) 



74-92 
78-96 

79-909 
83-80 

85-47 

87-62 

88-90 
91-22 

92-91 
9594 

199] 
101-7 

102-90 
106-4 

107-870 
112-40 

114 82 
118-69 



147 



Mass numbers of the isotopes 



69. 70. 71, 72. 73, 74, 7S (100%). 
76, 77, 78, 79 

70, 72, 73, 74 (0-87%). 75. 76 
(9-02%). 77 (7-58%),78 (23-52%), 
79, 80 (49-82%), 81, 82 (919%), 

83 84 

74. 75, 76. 77, 78, 79 (50-52%). 80, 
81 (49-48%), 82, 83, S4, 85, 87, 
88.89 

76, 77. 78 (0-354%). 79,80 (2-27%). 
81, 82 (11-56%). 83 (11-55%). 

84 (56-90%). 85. 86 (17-37%). 87, 

88, 89, 90, 91, 92, 93.94,95, 96, 
97 

81. 82, 83, 84. 85 (72-15%). 86, 87' 
(27-85%). 88, 89, 90, 91, 92, 93, 
94, 95, 97 

81, 82. 83, 84 (0-563%). 85. 86 
(9-86%). 87 (7-02%).88 («-S6%). 

89, 90, 91,92, 93,94,95.97 

82, 83, 84. 85. 86. 87. 88.89 (100 %). 

90,91,92,93,94.95.97 
86, 87, 88. 89, 90 (51-46%). 91 

(11-23%), 92 (1711%). 93, 94 

(17-4%), 95. 96 (2-8%). 97 
89, 90. 91. 92. 93 (100%). 94, 95. 

96, 97, 98. 99 
90.91. 92(15-86%). 93,94(912%), 

95 (15-70%), 96 (16-»%), 97 

(9-45%). 98 (23-75%), 99. 100 

(9-62%). 101, 102, 105 
92, 93, 94, 95, 96, 97, 91, 99. 100, 

101, 102, 105, 107 

94, 95, 96 (5-7%), 97. 98 (2-2%) 
99 (12-8%). 100 (12-7%). 10L 
(17-0%), 102 (31-3%). i03, 104 
(18-3%). 105, 106, 107 

95, 97. 98. 99, 100, 101, 102. 103 
(100%), 104, 105, 106, 107. 109 

100. 101, 102 (0-8%). 103, 104 
(9-3%). 105 (22-6%),10« (27-2%), 

107, 108 (26-8%). 109, 110 
(13-5%), HI, 112,113 

102, 103, 104, 105. 106. 107 
(51-35%), 108, 109 (48-65%). 
110,111, 112, 113, 114. 115 

104. 105, 106 (1-215%). 107. 108 
(0-875%), 109, 110(12-39%), 111 
(12-75%), 112 <24-«7%). 113 
(12-24%). 114(28-86%). 1 15. 116 
(7-58%), 117,118 

107, 108. 109, 110, 111, 112.113 
(4-23%). 114, 115* (»S-77%), 
116, i 17. 118, 119 

108. 111. 112 (0-9S%). 113. 1 

(0-65%), 115 (0-34%). 11 

(14-24%). 117 (7-57%). 

(24-01%), 119 (8-58%). 

(32-97%) 121, 122 (4-71%) 

124(5-98%), 125, 126. 127 




TABLE OF ISOTOPES (continued) 



Atomic 

mmbet 



32 

53 
54 

55 

56 

57 



59 
60 




Ulcmc.il 



SI Antimony 



Tellurium 

Iodine 
Xenon 

Caesium 
Barium 

Lanthanum 



Symbol 



Sb 
Te 



58 , Cerium 



Xe 

Cs 
Ba 

La 
Ce 



Praseodymium Pr 
Neodymium Nd 



61 Promclhium 

62 Samarium 

63 Europium 
Gadolinium 

Terbium 
Dysprosium 



Pm 
Sm 

Eu 
Gd 

Tb 



Atomic 



(C 



wcifht 
:=■ 12-00) 



121-75 
127-60 

126-90 
131-3 

132 90 
137-34 

138-91 

14012 

140-91 
144-24 

1147] 
150-35 

152-0 
157-25 

158-92 
162 50 

148 



Mnss numbers of the isotopes 



116, 117, 118. 119, 120, 121 
(57-25%}. 122. 12J (42-75%), 
124, 125. 126, 127, 129, 130, 131, 
132, 133, 134, 135 

117, 118. 119, 120 (0-089%), 121, 
122 (2-46%). 123 (0-87%), 124 
(4-61%). i25 (6-99%). 126 
(18-71%), 127. 128(31-79%),129. 
130(34-49%). 131, 132. 133,134, 

119, 120. 121. 122, 123, 124,125, 
26, 127 (100%). 128, 129. 130. 
j^ ; HI- 1 ". 'H 135. 136-, 137.- 

121. 122, 123, 124 (0-096%), 125. 
126 (0-09%). 127. 128 (1-919%), 
129 (26-44%), 130 (408%), 131 
(2118%). 132 (26-89%), 133. 
134 (10-44%), 135, 136 (8-87%), 
137. 138, 139, 140, 141, 143. 144 

123. 125, 126. 127, 128, 129, 130, 
131. 132. 133 (100%), 134, 135 
136, 137, 138, 139, 141, 142. 143, 

126 127. 128, 129, 130 (0-101%), 
SkJP (0-097%). 133. iS4 
2-42%). 13S $-59%), 136 
(7-81%), 137 (U-32%). 138 
(71-66%). 139. 140, 141, 142, 143, 
144 

131. ,132.13) 134, 135, 136. 137, 

!^.r! 9 42 / : ) i43fU 99 ^ ,,%) - 

'".134, 135. 136 ft-193%). 137, 
138 (0-25%). 139. 140 (8848%) 
"I, 142 (11-07%). 143 144.146 

l3 A:P 6 - l37 . '38. 139, 140. 141 
(100%). 142, 143,144, 146 

138, 139, 140. 141, 142 (27-13%). 

^■l 12 ; 20 .-;- 144 (23-87%)Ti4k 

(8-30%). 146 (17-18°;,). 147 148 
(5-72%). 149, ISO- (S-10%), 151 

'^.Wso.'TV^' 47 - 

^%). '«. 154(22-53%): 155, 

'•«•'«. 146, 147 148. 149, ISO, 
151(47-77%). 152,153(52-23%) 
154, 155, 156, 157", 158,159 ' 

148. 149. 150. 151. 152 (0-20»I) 

}2$ SZiVYll' ,S7 ('5-6(1%), 1S8 
, ^•?7%). '». 160(21-90% 161 

149. 151. 153, 154, 155. 156 157 
.Jfi&SSi?'- 160 *' 61 .. '62.163' 
'] gp4^» 



TABLE OF ISOTOPES (continued) 



Atomic 
number 



QOMOl 



67 Holmhim 

68 Erbium 

69 Thulium 



70 



71 

72 



73 
74 



75 



Ytterbium 



Lutecium 

Hafnium 



Tantalum 

Wolfram 

(Tunjstcn) 



MmbJqoi 



76 I Osmium 



77 Iridium 



78 

79 
80 

81 
82 

83 



r'.'rlrMi.n 

Gold 

Mercury 

Thallium 
Lead 

MMh 



Symbol 



Atomic 
weight 

(C--- 12-00) 



Ho 
Er 

Tm 
Yb 

La 
Hf 

Ta 
W 

Re 
Os 

Ir 
Pi 

Au 
Hg 

Tl 
Pb 

Bl 



164-93 
167-26 

168-93 
17304 

17497 
178-49 

180-95 
183-85 

186'20 
190-2 

192-2 
195W 

1970 

200-59 

204-37 
20719 

203-98 



Mass numbers of the isotopes 



160, 161, 162, 163, 164,165(100%). 

166 
160, 161, 162 (0-136%). 163. 164 

(l-56%), 165, 166 (33-41%). 167 

(22-94%). 168 (27-07%), 169, 

170(14-88%). 171 _ 

165, 166, 167, 163. 169 (100%), 170, 

171, 172 
166, 168 (0-14%),169, 170 (303%). 

171 (14-31%), 172 (21-82%). 173 

(16-13%). 174 (31-84%), 175, 

176 (12-73%), 177 
170. 171. 172, 173, 174, 17S 

(97-4%), 176- (2-6%). 177 
170. 171. 172. 173, 174 (0-18%), 

175, 176 (S-1S%), 177 (18-39%). 

178 (27-08%). 179 (13-78%), 180 

(35-44%). 181 
176. 177, 178, 179, 180* (0-0123%), 

181 (99-988%), 182. 183, 184, 185 
176. 177. 178. 179. 180 (0135%). 

181. 182 (26-4%). 183 (14-4%). 

184 (30-6%). 185. 186 (28-4%). 

187. 188 
180, 182. 183. 184. 185 (37-07%), 

186, 187* (62-93%), 188, 189 
182. 183, 184 (0-018%). 185, 186 
188 
190 
193, 

194 

187, 188, 190, 191 (38-5%), 192, 
193 (61-5%), 194, 195, 196. 197, 
198 

188, 190* (0-012%). 191, 192 

§•78%). 193. 194 (32-8%). 195 
3-7%;. 196 (25-4%), 197, 198 
■23%), 199 
191. m, 193. 194, 195, 196. 197 
(100%)^ 198. 199, 200, 201, 202. 

189, 190, 191, 192. 193, 194. 195, 
196 (0146%). 197. 198 (10-02%) 
199 (16-84 %), 200 (23-13%), 201 
(13-22%), 202 (29-80%), 203, 204 
(6-8S%). 205 

196, 197. 198, 199, 200. 201. 202. 
203 (295%). 204. 205 (70-5%), 
206. 207* (AcO, 208* (ThC), 
209, 210* (RaCT) 

198. 199, 200, 201, 203. 204 
(1-48%), 20* (23-6%). 207 
(22-6%). 208 (52-3%). 209, 210* 
(RaD). 211" (AcB). 212- (HiB), 
214* (RaB) 

198. 199, 200. 201. 202, 203, 204, 
205. 206. 207, 209 (100%' * 
(RaE). 211* (AcO. 212* 
213, 214' (RaC), 215 



10*. iw, *o* \v-vio ;.,,*. io->, 

(I-S9%), 187 (1-64%), 
(13-3%). 189 (16-1%). 
(26-4%), 191, 192 (41-0%). 



149 




TABLE OF ISOTOPES {continued) 



Atomic 
number 



84 

85 

86 

17 
(8 

89 
90 

91 

92 

93 

94 

95 

96 

97 
98 

99 

100 
101 
102 
103 



Element 



Polonium 

Astatine 

Radon 

Francium 
Radium 

Actinium 
Thorium 

Protactinium 

Uranium 

Neptunium 

Plutonium 

Amcricium 

Curium 

Bcrkcliura 
Californium 

Einsteinium 

Fcrmium 

Mendclevium 

Nobeliom 

Lawrcncium 



Symbol 



Po 



AC 

lEm) 
Fr 
Ra 

Ac 
Th 

Pa 

U 

Np 

Pu 

Am 

Cm 

HI. 
Cf 

B 

Fm 

Mv 

No 

Lw 



Atomic 

weight 

(C- 1200) 



[210) 

1210) 

[222] 

[223] 
22605 

227 

23204 

[231) 

23803 

[237] 
[242] 
[243] 
[247] 

BSI 



254 

253 
256 

257 



Mass numbers of the isotopes 



200. 201, 202. 203. 204, 205, 206. 

207. 2U8. 209, 210*. 211" (AcC'l, 

212* (ThC), 21.1, 214' (RnCO 

21S« (AcA), 216* (ThA), 217. 

218 (RaA) 
203, 204 205. 206. 207. 208, 209, 

210, 211, 212, 213. 214, 215*. 

216*. 217. 218*. 219" 
208. 209. 210, 211, 212. 215, 216, 

217. 218, 2I9« (An). 220* (Tn), 

221, 222' (Rn) 

211, 212, 217, 218, 219,220, 221. 

222. 223* (AcK) 

213,219 220, 22 1. 222, 223* (AcX), 
224* (ThX). 225. 226', 227, 228* 
(MsThi). 229. 230 

221. 222, 223, 224,225. 226. 227*, 
228- (MsTh2), 229, 230 

223 224, 225. 226. 227- (RdAc), 
228* (RdTh). 229. 230- (lo). 231 * 
(UY).232\233,234'(UX1I.235 

225. 226. 227. 228. 229, 230, £)1«. 
g2.?33,234'(UX2).234MUZ) 

227, 228, 229. 230, 231. 232, 233, 

234«(UD,235«(AcU),236.237 

238* (Ul). 239, 240 
231, 232. 233. 234, 235, 236, 237. 

238. 239. 240. 241 
232, 234 235. 236. 237. 238. 239(t), 

240.241.242.243,244 

237. 238, 239. 240. 241, 242, 243, 

238, 239. 240. 241, 242, 243, 244. 
245, 246. 247. 248 

243, 244. 245, 246, 247, 249 

244. 245. 246. 247, 248, 249, 250. 
251,252.253 ' 

246, 247, 253. 254. 255 

254. 255, 256 

256 



(t) This isotope has been found in pitchblende to a concentration of I port in 10". 




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ENERGY EQUIVALENTS 




Einstein's relation E = mc 2 relates mass and energy with 
the square of the speed of light as the constant of proportion- 
ality. Thus the energy equivalent of 1 g. of any substance 
is 8-988 x 10 20 ergs - 8-988 X 10 13 joules = 2-497 X 10 7 
kilowatt-hours. This amount of energy would be liberated if 
1 g. of matter was annihilated. 

It is often convenient to consider energies in terms of 
electron-volts (e.v.). One electron volt is the energy gained 
by any singly charged particle (such as an electron) in falling 
through a potential difference of 1 volt. 

One volt -- 10 8 e.m.u. of potential and the electronic 
charge is 1-602 X 10 -20 e.m.u. So the energy of 1 e.v. = 
10 s X 1-602 X 10- 20 = 1-602 X 10- 12 erg. 

1 k.e.v. = 1000 e.v. 1 M.e.v. = 10 9 e.v. 

For gas atoms in thermal equilibrium with one another 
the energy per degree of freedom is \kT, where k is Boltz- 
mann's constant and T is the absolute temperature. For an 
atom with three degrees of freedom, the energy is |&T. For 
molecules there are more than three degrees of freedom in 
general. This relation is not valid for temperatures near the 
absolute zero where quantum considerations enter. In 
chemistry and in thermodynamics energies arc often in 
terms of kT. In the table below the energy equivalent of one 
degree absolute is calculated from E = kT. 

The table given on p. 155 is suitable for converting most- 
of the commonly encountered energy units. It gives equiva- 
lent quantities in horizontal lines. Thus I g. = 8-988 X 10 20 
ergs = 1-098 x 10 27 electron masses = 6025 x 10 M a.m.u. 
= 5-610 x 10 28 M.e.v. = 6-511 x 10 36 deg. abs. etc. 

The table may be further extended to include the energy- 
frequency and the energy-wave number relation of photons 

through E = hv and E = hcCA, where j is the wave num- 
ber. Thus a photon of unit frequency has an energy of 
6-625 X 10 -27 erg while one having unit wave number has 
an energy of 1-986 x 10 -18 erg. 



154 



OPTICAL DATA 

REFRACTIVE INDEX OF GASES 





for D line 


= 5893 A. 




Acetylene 


1-000606 


Hydrogen 


1-000138 


Air 


1-000292 


Hydrogen chloride 


1-000447 


Ammonia 


1000375 


Hydrogen sulphide 


1-000630 


Argon 


1-000281 


Methane 


1-000441 


Carbon dioxide 


1-000450 


Nitric oxide 


1-000297 


Carbon monoxide 


1-000334 


Nitrous oxide 


1000515 


Chlorine 


1000768 


Nitrogen 


1-000297 


Cyanogen 


1-000800 


Oxygen 


1-000272 


Ethylene 


1-000674 


Sulphur dioxide 


1-000660 


Helium 


1-000036 


Water vapour 


1-000254 


REFRACTIVE 


INDICES 


(AGAINST AIR) FOR 




MEAN D LINE 






A = 5893 x 


10 -'cm. 




Canada Balsam 


1-53 


Iceland Spar (ord.) 
Iceland Spar (ext.) 


1-658 


Crown Glass 


1-48-1-61 


1-486 


Diamond 


2-417 


Quartz (ord.) 


1-544 


Felspar 


1-52 


Quartz (ext.) 


1-553 


Flint Glass 


1-53-1-96 


Rock Salt 


1-544 


Fluorspar 


1-434 


Ruby 


1-76 


Ice 


1-31 


Sylvine (KC1) 


1-490 


Water 


1-333 


Perspex 


1-495 



WAVELENGTHS OF IMPORTANT SPECTRAL 
LINES IN AIR AT 15° C AND 760 mm. 

A. = 10-* cm. = Angstrom unit 

Line Wavelength Line 




Kred 

0„d{CA> 

Li red 

Ha red (Q 

Cdred* 

Li orange 

Na orangc/(D,) 

Na orange l(DJ 

He yellow (Dj) 

Tl green 

Fe and Ca green (E) 



Wavelength 

A 

7668 

7594 

6870 

6708 

6563 

6438-4696 

6104 

5895-9 

58900 

5875-6 

5351 

5270 

• Accepted 



f(6.) 
Mg green{ «>,) 

l(6J 
Cd green* 
H0 blue-green (F) 
Cd blue* 
Sr blue 
Li blue 
H y blue(G l ) 
Fe and Ca blue (G) 
Ca blue (g) 
K violet 

standard lines 



Wavelength 

A 

5178 

5173 

5167 

5085-82 

4861 

4799-91 

4608 

4602 

4340 

4308 

4227 

4047 



Rydberg's Constant - Hydrogen, 109677-58; Helium, 109722-27 

Velocity of Light in Vacuum (c) = 299793 ± 0-5 km./s. 

156 









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157 




ACOUSTIC DATA 



VELOCITY OF SOUND 



Substance ! Temp. 


m./s. 


It/*. 


Substance 


m./s. 


ft./.. 


Air 

Hydrogen 

Qdbbd 

Water 
Oak (alone 

fibre) 
Class 


0°C 

o*c 

o°c. 

20° C 

10*-20° C 
IO°-20" C. 


331-3 

127(10 

317 

1410 

3850 
5000-6000 


1087 
4166 

IU--.0 
4626 

12630 
16400-19700 


Aluminium 
Brass 
Copper 
Iron 

Lead 
Mercury 


5100 
3500 
3600 
5000 

1300 
1452 


16730 
11480 
11810 
16400 

4265 
4764 



LOUDNESS OF SOUNDS 



Intensity in terms of 








threshold-intensity » 
•0002 dyne per cm.' 


Intensity in decibels 


Loudness in phons 




1 
10 



10(1 be!) 


Threshold of hearing 
10 Virtual silence 




10" 


20 


20 Quiet room 




10' 


30 


30 Watch ticking at 3 ft. 




10' 


40 


40 Quiet street 




10" 


50 


50 Quiel conversation 




10* 


60 


60 Quiet motor at 3 ft. 




IC 


70 


70 Loud conversation 




10* 


80 


80 Door slamming 




10" 


90 


90 Busy typing room 




10'« 


100 


100 Near loud motor horn 




10" 


110 


1 10 Pneumatic drill 




10" 


120 


120 Near aeroplunc engine 




10" 


130 


130 threshold of pain 





Limits of Audibility - Between 30 and 30,000 c/s. (approximately). 






MUSIC 




The consonant frequency intervals. 




Name 
Frequency Ratio 


Octave Fifth Fourth Major Major 
Third Sixth 
1:2 2:3 3:4 4:5 3:5 

Musical Scales - Vibration Ratios 


Minor Mtim 

Third SIjciH 

5:C 5:1 


C 

Basic* 1 24 
Scale / 1000 


D B F O A 

27 30 32 36 40 
1125 1-250 1-333 1-500 1667 


B C 
45 48 

1-875 2006 


Intervals — 


9 10 16 9 10 » 
8 9 15 8 9 8 


16 
15 



GEOMETRICAL MENSURATIONS 

(Illustrated) 




Area of Rectangle 
Area of rectangle equals LENGTH X WIDTH. 




• The Basic Scale is frequently referred to as the Natural or Diatonic Scale, 



158 



Area of Triangle 

Area of any triangle equals the length of the base muliiplied by half the 
vertical height. 

i.e. If A equals length of base and B equals vertical height, area equals 
A x B 



159 





Area of Parallelogram 

Area of a parallelogram equals the length of one of the sides multiplied 
by the perpendicular height. 

i.e. If A equals length of one side and B equals perpendicular height, 
area equals A x B. 





•H 



Area of Circle 

Area of a circle is proportional to the square of its radius. 

i.e. If R equals the radius of the circle, area equals irR' (tt, a constant 

22 
quantity = •=- or 31416). 



B 

Area of Trapezoid 



H 





Area of a trapezoid equals half the sum of the two parallel sides multi- 
plied by the perpendicular distance between them. 

I.e. If A and B equal the lengths of the two parallel sides and C equals 
the perpendicular distance between them, area equals — y — x C. 

160 



Determination of Height, Base, or Hypothenusc of a Right-angled 
Triangle 

If AB = height, BC = base, and AC = hypothenuse, when two 
dimensions are given : 

Base = VAC 5 - AB ! Height = VAC S - BC S 
Hypothenuse = \/BC a + AB 1 

161 





Area of Trapezium 
Area of a trapezium equals the length of the diagonal multiplied by half 
the sum of the perpendiculars let fall upon it from its opposite angles, 
i.e. If AB equals the length of the diagonal and CD + EF equals the 
sum ol the perpendiculars to the opposite angles, area equals 

AB x SpP 




Area of Ellipse 

Area of an ellipse equals half the larger axis multiplied by half the 

smaller axis and multiplied by t. 

i.e. If AB be the larger axis and d be half of it: and if CD be the smaller 

axis and e be the half of it, area equals dx ex n. 

An approximate formula for the Circumference of an ellipse is 





Area of Sector of Circle 

Area of sector of circle equals area of the full circle multiplied by the 
degrees in ARC and divided by 360. 

i.e. If R equals radius and C equals degrees in ARC, area equals 
R* x g x C 
360 ' 

162 




Area of Regular Polygon 

Divide the polygon into triangles; find the area of one triangle and 
multiply by the number of triangles contained in the polygoo. 

163 






Area of Segment of a Circle 
If a equals height of segment and b equals length of cord, area equals 



a x 2 x b 






2xy 



=H 



h t- 

To find the diameter of the Circle to which any Segment may belong. 
Square half the cord, then divide it by the height of the segment; now 
add this to the height of the segment. 

d* 

i.e. Diameter equals re. 

c 



164 




Area of Pyramid 

Multiply the perimeter of the base by half the slant height, now add the 
area of the base. 




Area of Sphere 

Area of a sphere equals four times the area of tbe diametrical section, 
i.e. If r equals radius, area equals 4 x r* x w. 



165 



I 




Area of Surface of a Cone 

Area of surface of a cone equals the circumference of the base multiplied 
by one-half the slant height of the cone added to the area of the base. 
i.e. If ab is the slant height, be the diameter and bd the radius of the 
base, area equals — * X -^ + («*)' x w . 





If a point in a circle be unwound and extended in a straight line, the 
path of the point will form an involute curve. 

To construct an involute - oex is the circle and 06 is a tangent equal in 
length to half the circumference of the circle. Now divide both the 
tangent and the semi-circle into any number of equal parts. From these 
points on the circle, a, b, c, d, e, draw tangents to the circle, a\, til, c3, 
etc., equal in length to o\, oi, tii, etc., respectively. The curve is then 
described by joining the terminus of each tangent. 



Area of die curved surface of the Frustum of a Cone 

To determine the area of the above, multiply half the sum of the 
diameters of the two circular ends by -n, now multiply this by the slant 
height of the frustum. 

i.e. If b, c, d, e is the frustum, be and de the two diameters, and bd the 

slant height, area equals — 5 — - x n x bd. 



166 



167 



1 



SURFACES AND VOLUMES 
OF SOLIDS 

S = Lateral or Convex Surface. V = Volume 




Parallelopiped 
S = P/. P is perimeter perpendicular to sides: / is lateral length. 

V = BH. B is area of base; H is perpendicular height. 

V = A/. A is area of section perpendicular to sides : / is lateral length. 




Cylinder, Right or Oblique, Circular or Elliptic, etc. 
S = PH. P is perimeter of base: H is perpendicular height. 
S = P|/. Pi is perimeter perpendicular to sides: / is lateral length. 

V = BH. B is area of base: H is perpendicular height. 

V = A/. Aisarea of section perpendicular to sides: /is lateral length. 




Prism, Right or Oblique, Regular or Irregular 
S =« PI. P is perimeter perpendicular to sides: / is lateral leng-.h. 

V — BH. B is area of base: H is perpendicular height. 

V = A/. A is area of section perpendicular to sides: /is lateral lergih. 



168 




Frustum of any Prism or Cylinder 

BH. B is area of base: H is perpendicular height from base to 
centre of gravity of top. 



V = JA(/, + /,), for cylinder. 



169 







Pyramid or Cone, Right and Regular 

S = JP/. P is perimeter of base: / is slant height. 

V = JBH. B is area of base: H is perpendicular height. 




Pyramid or Cone, Right or Oblique, Regular or Irregular 

V = jBH. B is area of base: H is perpendicular height. 

V = i volume of prism or cylinder of same base and perpendicular 

height. 

V = i volume of hemisphere of same base and perpendicular height. 




Frustum of Pyramid or Cone, Right and Regular, Parallel Ends 

g = j/(p + p) P and p are perimeters of base and top: / is slant 
height. 

V = iH(B + b + VBb). B and b are areas of base and top: H is per- 
pendicular height. 




Frustum of any Pyramid or Cone, Parallel Ends 

V = iH(B + b + V BbT- B and b are areas of base and top : H is per- 
pendicular height. 



170 



171 





Wedge, Parallelogram Face 

iDH(2A + B). A, B, A ate the lengths of the three edges: H is 
perpendicular height; D is perpendicular width. 



Spherical Sector 

S lrrR(4B + C) 

V - j*R'B 




V 



Prisma toid 

V = JHCB — b ■(- 4M). B and b are areas of base and top: H is per- 
pendicular height : M is area of section parallel 
to bases, midway between them. 

The Prismatoid formula applies also to any of the foregoing solids with 
parallel bases, to pyramids, cones, spherical sections, and to many 
solids with irregular surfaces. 




Spherical Segment 

S = 2»RB = W»B S i- C) 

V = i"B'(3R. - B) = tV*B(3C« + 4B«) 



172 



173 



—4 



i 



31 



c 1 

Spherical Zone 

S =2irRB 

V = V*"B(3A' + 3C« + 4B S ) 




Ungula of Right, Regular Cylinder 




Circular Ring 

S = 4w»Rr 
V = 2>r«Rr* 



Base = Segment BAB 



H 



S = (2RM - O X arc, BAB) ^tTq 



H 



V - «M' -Ox area, BAB) ^Tq 



Base = Half Circle 
S =2RH 

V = $R«H 




Base = Segment, CAC 



S -= (2RN + P x arc, CAQ 
V = (JN 1 + P x area, CAC) 



R + P 

H 

R + P 



V = JnR'H 



174 



175 




- B -H 



Ellipsoid 
V = *»rRAB 



NOTES 




InlA 



to two *(*» «* /» wax* 







Paraboloid 

V - i*R«H 

Ratio of corresponding volumes of a Cone, Paraboloid, Sphere, and 
Cylinder of equal height = J :j : $ :1. 

176 



NOTES 



NOTES 



NOTES 






Logarithms and anti-logarithms 
Sines and co-sines; tangents and 
co-tangents 

Seccants, co-seccants, and their 
logarithms 

Reciprocals, Napierian log- 
arithms 

Squares, Cubes and Roots 
The complete metric system with 
full conversion tables 
Speeds of Flow of Water, Tables 
of Density and Humidity 
Atomic Weights, the Properties 
of Solids, Liquids and Gases 
Information on Isotopes, radio- 
activity, energy equivalents, opti- 
cal and acoustical data 
Geometrical Mensurations, etc. 



This uniquely comprehensive 
volume of tablesand statistical 
information in physics and 
chemistry has been compiled 
to meet the needs of students, 
professionals and technicians 
over a wide field. It brings to- 
gether for the first time at a 
'paperback' price much impor- 
tant information usually only 
available in several different, 
and often expensive, volumes. 
Here it is all set out with an eye 
to maximum clarity and ease of 
use. 



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